Multiple Regression for Matrix and Vector Predictors: Models, Theory, Algorithms, and Beyond
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915098257260544 |
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| author | Lin, Meixia Zeng, Ziyang Zhang, Yangjing |
| author_facet | Lin, Meixia Zeng, Ziyang Zhang, Yangjing |
| contents | Matrix regression plays an important role in modern data analysis due to its ability to handle complex relationships involving both matrix and vector variables. We propose a class of regularized regression models capable of predicting both matrix and vector variables, accommodating various regularization techniques tailored to the inherent structures of the data. We establish the consistency of our estimator when penalizing the nuclear norm of the matrix variable and the $\ell_1$ norm of the vector variable. To tackle the general regularized regression model, we propose a unified framework based on an efficient preconditioned proximal point algorithm. Numerical experiments demonstrate the superior estimation and prediction accuracy of our proposed estimator, as well as the efficiency of our algorithm compared to the state-of-the-art solvers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19264 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiple Regression for Matrix and Vector Predictors: Models, Theory, Algorithms, and Beyond Lin, Meixia Zeng, Ziyang Zhang, Yangjing Optimization and Control Matrix regression plays an important role in modern data analysis due to its ability to handle complex relationships involving both matrix and vector variables. We propose a class of regularized regression models capable of predicting both matrix and vector variables, accommodating various regularization techniques tailored to the inherent structures of the data. We establish the consistency of our estimator when penalizing the nuclear norm of the matrix variable and the $\ell_1$ norm of the vector variable. To tackle the general regularized regression model, we propose a unified framework based on an efficient preconditioned proximal point algorithm. Numerical experiments demonstrate the superior estimation and prediction accuracy of our proposed estimator, as well as the efficiency of our algorithm compared to the state-of-the-art solvers. |
| title | Multiple Regression for Matrix and Vector Predictors: Models, Theory, Algorithms, and Beyond |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2410.19264 |